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Simultaneous inference for Berkson errors-in-variables regression under fixed design 固定设计下变量回归中Berkson误差的同时推理
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-30 DOI: 10.1007/s10463-021-00817-z
Katharina Proksch, Nicolai Bissantz, Hajo Holzmann
{"title":"Simultaneous inference for Berkson errors-in-variables regression under fixed design","authors":"Katharina Proksch,&nbsp;Nicolai Bissantz,&nbsp;Hajo Holzmann","doi":"10.1007/s10463-021-00817-z","DOIUrl":"10.1007/s10463-021-00817-z","url":null,"abstract":"<div><p>In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this paper we consider a nonparametric measurement error model of Berkson type with fixed design regressors and centered random errors, which is in contrast to much existing work in which the predictors are taken as random observations with random noise. Based on an estimator that takes the error in the predictor into account and on a suitable Gaussian approximation, we derive finite sample bounds on the coverage error of uniform confidence bands, where we circumvent the use of extreme-value theory and rather rely on recent results on anti-concentration of Gaussian processes. In a simulation study we investigate the performance of the uniform confidence sets for finite samples.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-021-00817-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50055206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonparametric tests for multistate processes with clustered data 具有聚集数据的多状态过程的非参数测试。
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-22 DOI: 10.1007/s10463-021-00819-x
Giorgos Bakoyannis, Dipankar Bandyopadhyay
{"title":"Nonparametric tests for multistate processes with clustered data","authors":"Giorgos Bakoyannis,&nbsp;Dipankar Bandyopadhyay","doi":"10.1007/s10463-021-00819-x","DOIUrl":"10.1007/s10463-021-00819-x","url":null,"abstract":"<div><p>In this work, we propose nonparametric two-sample tests for population-averaged transition and state occupation probabilities for continuous-time and finite state space processes with clustered, right-censored, and/or left-truncated data. We consider settings where the two groups under comparison are independent or dependent, with or without complete cluster structure. The proposed tests do not impose assumptions regarding the structure of the within-cluster dependence and are applicable to settings with informative cluster size and/or non-Markov processes. The asymptotic properties of the tests are rigorously established using empirical process theory. Simulation studies show that the proposed tests work well even with a small number of clusters, and that they can be substantially more powerful compared to the only, to the best of our knowledge, previously proposed nonparametric test for this problem. The tests are illustrated using data from a multicenter randomized controlled trial on metastatic squamous-cell carcinoma of the head and neck.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9455730/pdf/nihms-1779574.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9122668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inference for nonstationary time series of counts with application to change-point problems 非平稳计数时间序列的推理及其在变点问题中的应用
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-18 DOI: 10.1007/s10463-021-00815-1
William Kengne, I. S. Ngongo
{"title":"Inference for nonstationary time series of counts with application to change-point problems","authors":"William Kengne, I. S. Ngongo","doi":"10.1007/s10463-021-00815-1","DOIUrl":"https://doi.org/10.1007/s10463-021-00815-1","url":null,"abstract":"","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52265117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inference for nonstationary time series of counts with application to change-point problems 非平稳计数时间序列的推理及其在变点问题中的应用
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-18 DOI: 10.1007/s10463-021-00815-1
William Kengne, Isidore S. Ngongo
{"title":"Inference for nonstationary time series of counts with application to change-point problems","authors":"William Kengne,&nbsp;Isidore S. Ngongo","doi":"10.1007/s10463-021-00815-1","DOIUrl":"10.1007/s10463-021-00815-1","url":null,"abstract":"<div><p>We consider an integer-valued time series <span>((Y_t)_{tin {mathbb {Z}}})</span> where the model after a time <span>(k^*)</span> is Poisson autoregressive with the conditional mean that depends on a parameter <span>(theta ^*in varTheta subset {mathbb {R}}^d)</span>. The structure of the process before <span>(k^*)</span> is unknown; it could be any other integer-valued process, that is, <span>((Y_t)_{tin {mathbb {Z}}})</span> could be nonstationary. It is established that the maximum likelihood estimator of <span>(theta ^*)</span> computed on the nonstationary observations is consistent and asymptotically normal. Subsequently, we carry out the sequential change-point detection in a large class of Poisson autoregressive models, and propose a monitoring scheme for detecting change. The procedure is based on an updated estimator, which is computed without the historical observations. The above results of inference in a nonstationary setting are applied to prove the consistency of the proposed procedure. A simulation study as well as a real data application are provided.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50036052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution Cauchy分布拟算术平均的最大似然估计和一步估计的Bahadur效率
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-11 DOI: 10.1007/s10463-021-00818-y
Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe
{"title":"Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution","authors":"Yuichi Akaoka,&nbsp;Kazuki Okamura,&nbsp;Yoshiki Otobe","doi":"10.1007/s10463-021-00818-y","DOIUrl":"10.1007/s10463-021-00818-y","url":null,"abstract":"<div><p>Some quasi-arithmetic means of random variables easily give unbiased strongly consistent closed-form estimators of the joint of the location and scale parameters of the Cauchy distribution. The one-step estimators of those quasi-arithmetic means of the Cauchy distribution are considered. We establish the Bahadur efficiency of the maximum likelihood estimator and the one-step estimators. We also show that the rate of the convergence of the mean-squared errors achieves the Cramér–Rao bound. Our results are also applicable to the circular Cauchy distribution .</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-021-00818-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47546270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Multi-round smoothed composite quantile regression for distributed data 分布式数据的多轮平滑复合分位数回归
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-10 DOI: 10.1007/s10463-021-00816-0
Fengrui Di, Lei Wang
{"title":"Multi-round smoothed composite quantile regression for distributed data","authors":"Fengrui Di,&nbsp;Lei Wang","doi":"10.1007/s10463-021-00816-0","DOIUrl":"10.1007/s10463-021-00816-0","url":null,"abstract":"<div><p>Statistical analysis of large-scale dataset is challenging due to the limited memory constraint and computation source and calls for the efficient distributed methods. In this paper, we mainly study the distributed estimation and inference for composite quantile regression (CQR). For computational and statistical efficiency, we propose to apply a smoothing idea to the CQR loss function for the distributed data and then successively refine the estimator via multiple rounds of aggregations. Based on the Bahadur representation, we derive the asymptotic normality of the proposed multi-round smoothed CQR estimator and show that it also achieves the same efficiency of the ideal CQR estimator by analyzing the entire dataset simultaneously. Moreover, to improve the efficiency of the CQR, we propose a multi-round smoothed weighted CQR estimator. Extensive numerical experiments on both simulated and real data validate the superior performance of the proposed estimators.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43810037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes 基于平稳和遍历离散时间过程的函数导数估计的渐近性
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2022-01-04 DOI: 10.1007/s10463-021-00814-2
Salim Bouzebda, Mohamed Chaouch, Sultana Didi Biha
{"title":"Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes","authors":"Salim Bouzebda,&nbsp;Mohamed Chaouch,&nbsp;Sultana Didi Biha","doi":"10.1007/s10463-021-00814-2","DOIUrl":"10.1007/s10463-021-00814-2","url":null,"abstract":"<div><p>The main purpose of the present work is to investigate kernel-type estimate of a class of function derivatives including parameters such as the density, the conditional cumulative distribution function and the regression function. The uniform strong convergence rate is obtained for the proposed estimates and the central limit theorem is established under mild conditions. Moreover, we study the asymptotic mean integrated square error of kernel derivative estimator which plays a fundamental role in the characterization of the optimal bandwidth. The obtained results in this paper are established under a general setting of discrete time stationary and ergodic processes. A simulation study is performed to assess the performance of the estimate of the derivatives of the density function as well as the regression function under the framework of a discretized stochastic processes. An application to financial asset prices is also considered for illustration.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50008096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Empirical tail conditional allocation and its consistency under minimal assumptions 最小假设下的经验尾条件分配及其一致性
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2021-11-26 DOI: 10.1007/s10463-021-00813-3
N. V. Gribkova, J. Su, R. Zitikis
{"title":"Empirical tail conditional allocation and its consistency under minimal assumptions","authors":"N. V. Gribkova,&nbsp;J. Su,&nbsp;R. Zitikis","doi":"10.1007/s10463-021-00813-3","DOIUrl":"10.1007/s10463-021-00813-3","url":null,"abstract":"<div><p>Under minimal assumptions, we prove that an empirical estimator of the tail conditional allocation (TCA), also known as the marginal expected shortfall, is consistent. Examples are provided to confirm the minimality of the assumptions. A simulation study illustrates the performance of the estimator in the context of developing confidence intervals for the TCA. The philosophy adopted in the present paper relies on three principles: easiness of practical use, mathematical rigor, and practical justifiability and verifiability of assumptions.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-021-00813-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50049151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fixed accuracy estimation of parameters in a threshold autoregressive model 阈值自回归模型中参数的固定精度估计
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2021-10-18 DOI: 10.1007/s10463-021-00812-4
Victor V. Konev, Sergey E. Vorobeychikov
{"title":"Fixed accuracy estimation of parameters in a threshold autoregressive model","authors":"Victor V. Konev,&nbsp;Sergey E. Vorobeychikov","doi":"10.1007/s10463-021-00812-4","DOIUrl":"10.1007/s10463-021-00812-4","url":null,"abstract":"<div><p>For parameters in a threshold autoregressive process, the paper proposes a sequential modification of the least squares estimates with a specific stopping rule for collecting the data for each parameter. In the case of normal residuals, these estimates are exactly normally distributed in a wide range of unknown parameters. On the base of these estimates, a fixed-size confidence ellipsoid covering true values of parameters with prescribed probability is constructed. In the i.i.d. case with unspecified error distributions, the sequential estimates are asymptotically normally distributed uniformly in parameters belonging to any compact set in the ergodicity parametric region. Small-sample behavior of the estimates is studied via simulation data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43833447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-stage data segmentation permitting multiscale change points, heavy tails and dependence 允许多尺度变化点、重尾和相关性的两阶段数据分割
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2021-09-25 DOI: 10.1007/s10463-021-00811-5
Haeran Cho, Claudia Kirch
{"title":"Two-stage data segmentation permitting multiscale change points, heavy tails and dependence","authors":"Haeran Cho,&nbsp;Claudia Kirch","doi":"10.1007/s10463-021-00811-5","DOIUrl":"10.1007/s10463-021-00811-5","url":null,"abstract":"<div><p>The segmentation of a time series into piecewise stationary segments is an important problem both in time series analysis and signal processing. In the presence of multiscale change points with both large jumps over short intervals and small jumps over long intervals, multiscale methods achieve good adaptivity but require a model selection step for removing false positives and duplicate estimators. We propose a localised application of the Schwarz criterion, which is applicable with any multiscale candidate generating procedure fulfilling mild assumptions, and establish its theoretical consistency in estimating the number and locations of multiple change points under general assumptions permitting heavy tails and dependence. In particular, combined with a MOSUM-based candidate generating procedure, it attains minimax rate optimality in both detection lower bound and localisation for i.i.d. sub-Gaussian errors. Overall competitiveness of the proposed methodology compared to existing methods is shown through its theoretical and numerical performance.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10463-021-00811-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41852249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
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